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Mathematics 14 Online
kaylak:

calc help 4 questions

kaylak:

1 attachment
kaylak:

@Tranquility

kaylak:

still typing lol?

Karla:

First find the derivative of f'(x) For this you should watch this video till time 6.10 as I cannot explain through writing https://youtu.be/QqF3i1pnyzU So now you got the formula as f'(x)=nx^n-1 So for you question for x^2 n=2 And first 5x n=1 Apply in formula f'(x)=2x^2-1 + 1*5x^1-1 f'(x)=2x +5 So as they said x=4 Put 4 in 2(x)+5 It's f'(4)=2(4)+5 f'(x)=13

kaylak:

I thought so lol could you help with 3 more?

Karla:

Yep it would be great (:

kaylak:

1 attachment
kaylak:

-3?

Karla:

Yes

kaylak:

really why?

kaylak:

when I did difference quotient it was -3/1-h

kaylak:

they all appear to be symmetric quotients

Karla:

f'(x)=3/x That is same as f'(x)=3x^-1 So in this n=-1 Put in the formula f'(x)=nx^n-1 That is= -1*3x^-1-1 That is=-3*x^-2 That is same as -3/x^2 Put -1 in place of x -3/(-1)^2 -3/1=-3

kaylak:

this one is 0?

1 attachment
kaylak:

I'm fanning you lol so if I need further help I know who to tag lol

Karla:

Hahaha

Karla:

Wait m solving

Karla:

Does not exist

Karla:

D

kaylak:

just curious why is that?

kaylak:

1 attachment
Karla:

https://youtu.be/H-ybCx8gt-8

Karla:

Now the formula you got is (derivative of outside leaving the inside as it is) *(derivative of inside)

kaylak:

it looks like a cusp but could be a corner I'm thinking more cusp because it bends slightly

kaylak:

for the last question I say cusp

Karla:

n=1/5 Take the derivative of outside it is 1/5(x+1)^(1/5)-1 That is 1/5(x+1)^-4/5 Put value of x=-1 1/5(0)^-4/5 And O^-4/5 is math error solve on calculator so Derivative of this does not exist

kaylak:

okay cool

Karla:

Did you understand?

kaylak:

yes I did

Karla:

Okay great

kaylak:

is the last one cusp?

kaylak:

just curious college student?

Karla:

Yes college student and you?

kaylak:

I would say cusp because of the graph ty though and senior in hs lol

Karla:

K (:

Karla:

Sorry I don't know the answer for that question

kaylak:

it's okay

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